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href="#算法代码">算法代码</a><!----></li><!--]--></ul><!--[--><!--]--></aside><div class="sidebar-mask"></div><main class="page" data-v-7eddb2c4><div class="container" data-v-7eddb2c4><!--[--><!--]--><div style="position:relative;" class="content" data-v-7eddb2c4><div><h1 id="差分" tabindex="-1">差分 <a class="header-anchor" href="#差分" aria-hidden="true">#</a></h1><p>本算法题来自acwing 97. 差分 ,以下是要求</p><h2 id="要求" tabindex="-1">要求 <a class="header-anchor" href="#要求" aria-hidden="true">#</a></h2><p>输入一个长度为 n 的整数序列。</p><p>接下来输入 m 个操作，每个操作包含三个整数 l,r,c，表示将序列中 [l,r]之间的每个数加上 c。</p><p><strong>请你输出进行完所有操作后的序列。</strong></p><p>输入格式： 第一行包含两个整数 n 和 m 。</p><p>第二行包含 n 个整数，表示整数序列。</p><p>接下来 m 行，每行包含三个整数 l，r，c ，表示一个操作。</p><p>输出格式: 共一行，包含 n 个整数，表示最终序列。</p><p>输入样例： 6 3 1 2 2 1 2 1 1 3 1 3 5 1 1 6 1</p><p>输出样例： 3 4 5 3 4 2</p><h2 id="算法代码" tabindex="-1">算法代码 <a class="header-anchor" href="#算法代码" aria-hidden="true">#</a></h2><div class="language-js"><pre><code><span class="token keyword">const</span> <span class="token constant">N</span> <span class="token operator">=</span> <span class="token number">100010</span><span class="token punctuation">;</span>
<span class="token keyword">let</span> n<span class="token punctuation">,</span> m<span class="token punctuation">;</span>
<span class="token keyword">let</span> a <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token constant">N</span><span class="token punctuation">)</span><span class="token punctuation">;</span>  <span class="token comment">// 存储初始数组</span>
<span class="token keyword">let</span> b <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token constant">N</span><span class="token punctuation">)</span><span class="token punctuation">;</span>  <span class="token comment">// 存储差分数组</span>

<span class="token keyword">function</span> <span class="token function">insert</span><span class="token punctuation">(</span><span class="token parameter">l<span class="token punctuation">,</span> r<span class="token punctuation">,</span> c</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 将区间[l, r]中的元素加上c</span>
  b<span class="token punctuation">[</span>l<span class="token punctuation">]</span> <span class="token operator">+=</span> c<span class="token punctuation">;</span>
  b<span class="token punctuation">[</span>r <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">-=</span> c<span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">function</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 读入n,m</span>
  <span class="token keyword">let</span> input <span class="token operator">=</span> <span class="token function">readline</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">split</span><span class="token punctuation">(</span><span class="token string">&#39; &#39;</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">map</span><span class="token punctuation">(</span>Number<span class="token punctuation">)</span><span class="token punctuation">;</span>
  n <span class="token operator">=</span> input<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span> m <span class="token operator">=</span> input<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>  <span class="token comment">//控制台输入的值</span>

  <span class="token comment">// 读入初始数组a</span>
  input <span class="token operator">=</span> <span class="token function">readline</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">split</span><span class="token punctuation">(</span><span class="token string">&#39; &#39;</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">map</span><span class="token punctuation">(</span>Number<span class="token punctuation">)</span><span class="token punctuation">;</span>
  <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator">&lt;=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    a<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> input<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>

  <span class="token comment">// 对差分数组b进行预处理，初始化为初始数组a</span>
  <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator">&lt;=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token function">insert</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> i<span class="token punctuation">,</span> a<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>

  <span class="token comment">// 对m个操作进行处理</span>
  <span class="token keyword">while</span> <span class="token punctuation">(</span>m<span class="token operator">--</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    input <span class="token operator">=</span> <span class="token function">readline</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">split</span><span class="token punctuation">(</span><span class="token string">&#39; &#39;</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">map</span><span class="token punctuation">(</span>Number<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token keyword">let</span> l <span class="token operator">=</span> input<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span> r <span class="token operator">=</span> input<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> c <span class="token operator">=</span> input<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
    <span class="token function">insert</span><span class="token punctuation">(</span>l<span class="token punctuation">,</span> r<span class="token punctuation">,</span> c<span class="token punctuation">)</span><span class="token punctuation">;</span>  <span class="token comment">// 将区间[l, r]中的元素加上c</span>
  <span class="token punctuation">}</span>

  <span class="token comment">// 根据差分数组b求出最终数组c</span>
  <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">let</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator">&lt;=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    b<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">+=</span> b<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
  <span class="token punctuation">}</span>

  <span class="token comment">// 输出最终数组c</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>b<span class="token punctuation">.</span><span class="token function">slice</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> n <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">join</span><span class="token punctuation">(</span><span class="token string">&#39; &#39;</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
</code></pre></div><div class="language-"><pre><code>假设原始数组为 [4, 6, 7, 8]， 差分数组为 [4, 2, 1, 1]。

对差分数组 b 求前缀和，得到：

c[1] = b[1] = 4

c[2] = b[1] + b[2] = 6

c[3] = b[1] + b[2] + b[3] = 7

c[4] = b[1] + b[2] + b[3] + b[4] = 8

对比一下原始数组，可以看到：

第一项：a[1] = 4，而 c[1] = b[1] = 4，相同。

第二项：a[2] = 6，而 c[2] = b[1] + b[2] = 4 + 2 = 6，相同。

第三项：a[3] = 7，而 c[3] = b[1] + b[2] + b[3] = 4 + 2 + 1 = 7，相同。

第四项：a[4] = 8，而 c[4] = b[1] + b[2] + b[3] + b[4] = 4 + 2 + 1 + 1 = 8，相同。

所以可以发现，前缀和数组 c 就是原始数组 a，其差分数组 b 就是相邻两项之差。
···</code></pre></div></div></div><footer class="page-footer" data-v-7eddb2c4 data-v-fb8d84c6><div class="edit" data-v-fb8d84c6><div class="edit-link" data-v-fb8d84c6 data-v-1ed99556><!----></div></div><div class="updated" data-v-fb8d84c6><!----></div></footer><!----><!--[--><!--]--></div></main></div><!----><!--]--></div>
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